Question

A person invests 4000 dollars in a bank. The bank pays 6.25% interest compounded

annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 9600 dollars?

Answer 1

14.4

Explanation:

Given that :

Principal = 4000

Interest (r) = 6.25% compounded annually

Calculate time, t, if final amount A = 9600

Using the compound interest formula :

A = P(1 + r/n)^n*t

A = final amount

n = number of times interest is applied per period

9600 = 4000(1 + 0.0625)^t

9600 = 4000(1.0625)^t

9600/4000 = 1.0625^t

2.4 = 1.0625^t

Take the log of both sides

0.3802112 = 0.0263289t

t = 0.3802112/0.0263289

t = 14.440811

t = 14.4 ( nearest tenth)